Approximating the Region of Multi-Task Coordination via the Optimal Lyapunov-Like Barrier Function

We consider the multi-task coordination problem for multi-agent systems under the following objectives: 1. collision avoidance; 2. connectivity maintenance; 3. convergence to desired destinations. The paper focuses on the safety guaranteed region of multi-task coordination (SG-RMTC), i.e., the set of initial states from which all trajectories converge to the desired configuration, while at the same time achieve the multi-task coordination and avoid unsafe sets. In contrast to estimating the domain of attraction via Lyapunov functions, the main underlying idea is to employ the sublevel sets of Lyapunov-like barrier functions to approximate the SG-RMTC. Rather than using fixed Lyapunov-like barrier functions, a systematic way is proposed to search an optimal Lyapunov-like barrier function such that the under-estimate of SG-RMTC is maximized. Numerical examples illustrate the effectiveness of the proposed method.